Uploaded July 2019 | Updated September 2026, 2 weeks ago

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Laguerre's method for finding real and complex roots of polynomials. Includes history, derivation, examples, and discussion of the order of convergence as well as visualizations of convergence behavior. Example code available on github github.com/osveliz/numerical-veliz

Chapters
00:00 Intro
00:20 Sources
00:44 Derivation
03:08 Laguerre's Method
03:52 K. A. Redish
04:13 Visuzliation
05:24 Forman S. Acton
06:05 Example
07:04 Example 2
07:43 Example 3
08:01 Convergence
8:35 Laguerre Fractal
10:05 Summary
10:34 Thank You

Further Viewing:
Newton's Method youtu.be/E24zUEKqgwQ
Horner's Method youtu.be/zEvfkSuPqWk
Newton Fractals youtu.be/MWD2A0Vg2V0
Aberth-Ehrlich Method youtu.be/XIzCzfMDSzk
Halley's Method and Fractal youtu.be/3WiVGSy_084
Householder's Method and Fractal youtu.be/F9DFewL0mho
Bairstow's Method youtu.be/iUGEk6kngFw

Reference Links:
"Racines d'une Équation Algébrique" by Laguerre babel.hathitrust.org/cgi/pt?id=miun.aan9493.0001.001&view=1up&seq=103
"On Laguerre's Method" by K. A. Redish tandfonline.com/doi/abs/10.1080/0020739740050112
"Numerical Methods That Work" by Forman S. Acton books.google.com/books?id=cGnSMGSE5Y4C&lpg=PP1&pg=PA187#v=onepage&q&f=false